User:Ganaram inukshuk/Notes/TAMNAMS
This is a subpage for TAMNAMS-related notes, containing various proposals of varying degrees of usefulness and other useful things. This also contains rewrites of sections of the main TAMNAMS page that aren't quite ready to be deployed.
Sandboxed section: Naming mos modes
The easiest way to name the modes of a mos, without having to memorize any names, is to refer to them by their UDP, which refers to how many generators are stacked above and below the tonic to produce a mode of the mos.
This section's running example is 5L 3s, whose brightest mode is LLsLLsLs.
Simplified UDP notation
Normal UDP notation is summarized below:
- For single-period mosses, the UDP is notated as u|d, where u is the number of bright generators stacked above the tonic, d is the number of bright generators stacked below the tonic, and "|" is pronounced as "pipe". The full name of a mos's mode is xL ys u|d.
- For multi-period mosses with p periods, the UDP of is notated as up|dp(p). Since there are generators being stacked above and below every period - not just the tonic - there are in total u times p and d times p generators being stacked above and below their respective starting pitches. The full name in this case is xL ys up|dp(p).
To make notation easier, TAMNAMS makes the following modifications to UDP notation:
- The UDP for multi-period mosses may be written as u|d(p) rather than up|dp(p). This is because the period already appears in both the quantity of bright (u times p) and dark (d times p) generators, so omitting the p term makes the notation less redundant. In contexts where it doesn't cause confusion, the notation can be simplified further to u|d.
- The UDP for a mode may be shortened to "u|" under the reasoning that omitting the d term, which can be inferred by the u term, makes the notation less redundant. For example, "5L 3s 5|", which refers to LsLLsLLs, is read as "5 ell 3 ess 5 pipe".
- The shortened notation of "u|" is sufficient in most cases, but in situations where it makes more sense to think in terms of the dark generator, such as with a mos whose dark generator is the bright generator of a related mos, the notation is instead "|d".
This simplified notation will be used throughout this section, unless otherwise specified. In any case, the name of a mos can be substituted for its xL ys form.
Finding mos modes
Rotating the sequence of steps - that is, moving the step at the beginning to the end - produces a different mode. This can be repeated until the initial mode that was started with is produced.
This rotation process usually returns the modes in rotational order, not by brightness. To get the modes in order by brightness, produce every interval for each mode - starting at the mosunison and ending at the mosoctave - producing an interval matrix. The brightest mode will be the mode that has all of its intervals - excluding the mosunison, mosoctave, and mosperiods if multi-period - in its large size. The 2nd-brightest mode will have one interval in its small size - for multi-period mosses, one interval is in its small size for every instance of the mosperiod - and so on. The darkest mode will have all of its intervals in its small size. A much faster way to do this process is to skip making an interval matrix and sort the modes produced by rotation in alphabetical order, effectively sorting all modes by decreasing brightness. In either case, the UDP for the modes sorted by brightness are (n-1)|0, (n-2)|1, and so on to 0|(n-1), or (n-1)|, (n-2)| to 0|. The table below shows the modes produced rotationally, and can be sorted by UDP.
| Mode | Rotational order | Simplified UDP | mosunison | 1-mosstep | 2-mosstep | 3-mosstep | 4-mosstep | 5-mosstep | 6-mosstep | 7-mosstep | mosoctave |
|---|---|---|---|---|---|---|---|---|---|---|---|
| LLsLLsLs | 0 | 7| | 0 (perfect) | L (major) | 2L (major) | 2L+s (perfect) | 3L+s (major) | 4L+s (augmented) | 4L+2s (major) | 5L+2s (major) | 5L+3s (perfect) |
| LsLLsLsL | 1 | 4| | 0 (perfect) | L (major) | L+s (minor) | 2L+s (perfect) | 3L+s (major) | 3L+2s (perfect) | 4L+2s (major) | 4L+3s (minor) | 5L+3s (perfect) |
| sLLsLsLL | 2 | 1| | 0 (perfect) | s (minor) | L+s (minor) | 2L+s (perfect) | 2L+2s (minor) | 3L+2s (perfect) | 3L+3s (minor) | 4L+3s (minor) | 5L+3s (perfect) |
| LLsLsLLs | 3 | 6| | 0 (perfect) | L (major) | 2L (major) | 2L+s (perfect) | 3L+s (major) | 3L+2s (perfect) | 4L+2s (major) | 5L+2s (major) | 5L+3s (perfect) |
| LsLsLLsL | 4 | 3| | 0 (perfect) | L (major) | L+s (minor) | 2L+s (perfect) | 2L+2s (minor) | 3L+2s (perfect) | 4L+2s (major) | 4L+3s (minor) | 5L+3s (perfect) |
| sLsLLsLL | 5 | 0| | 0 (perfect) | s (minor) | L+s (minor) | L+2s (diminished) | 2L+2s (minor) | 3L+2s (perfect) | 3L+3s (minor) | 4L+3s (minor) | 5L+3s (perfect) |
| LsLLsLLs | 6 | 5| | 0 (perfect) | L (major) | L+s (minor) | 2L+s (perfect) | 3L+s (major) | 3L+2s (perfect) | 4L+2s (major) | 5L+2s (major) | 5L+3s (perfect) |
| sLLsLLsL | 7 | 2| | 0 (perfect) | s (minor) | L+s (minor) | 2L+s (perfect) | 2L+2s (minor) | 3L+2s (perfect) | 4L+2s (major) | 4L+3s (minor) | 5L+3s (perfect) |
Since multi-period mosses repeats every period rather than at every octave, the number of modes corresponds to the number of pitches in the period. As a result, multi-period mosses always have fewer modes. An example is shown for 3L 6s, with modified UDPs as described in the previous section.
| Mode | Mode name | Simplified UDP | Rotational order | mosunison | 1-mosstep | 2-mosstep | 3-mosstep | 4-mosstep | 5-mosstep | 6-mosstep | 7-mosstep | 8-mosstep | mosoctave |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| LssLssLss | 3L 6s 2| | 2| | 0 | 0 (perfect) | L (augmented) | L+s (perfect) | L+2s (perfect) | 2L+2s (augmented) | 2L+3s (perfect) | 2L+4s (perfect) | 3L+4s (augmented) | 3L+5s (perfect) | 3L+6s (perfect) |
| sLssLssLs | 3L 6s 1| | 1| | 2 | 0 (perfect) | s (perfect) | L+s (perfect) | L+2s (perfect) | L+3s (perfect) | 2L+3s (perfect) | 2L+4s (perfect) | 2L+5s (perfect) | 3L+5s (perfect) | 3L+6s (perfect) |
| ssLssLssL | 3L 6s 0| | 0| | 1 | 0 (perfect) | s (perfect) | 2s (diminished) | L+2s (perfect) | L+3s (perfect) | L+4s (diminished) | 2L+4s (perfect) | 2L+5s (perfect) | 2L+6s (diminished) | 3L+6s (perfect) |
Alterations to a mode
Alterations to a mode are denoted by listing what 0-indexed mosdegrees are altered by one or more moschromas, using accidentals whose meaning and notation is made clear. As a diatonic example, mixolydian b6 can be written as 5L 2s 5| b6 (where the 6th degree is is a ordinal-indexed 6th, not a 0-indexed mosdegree), but for a non-diatonic example, mode 5| of 5L 3s with a 4-mosdegree lowered by a chroma is written as "5L 3s 5| @4d" (read as "5L 3s 5 pipe at-4-degree", where the "at/@" accidental is from diamond-mos notation).
Named mos modes
Many people, or groups of people, who have described individual mosses have independently came up with names for the mos's modes. The mosses listed below have named mos modes on their respective pages. (todo: add links)
- 5-note mosses: 4L 1s
- 7-note mosses: 1L 6s, 2L 5s, 3L 4s, 4L 3s, 5L 2s, and 6L 1s
- 8-note mosses: 3L 5s, 5L 3s, and 7L 1s
- 9-note mosses: 5L 4s and 7L 2s
- 10-note mosses: 3L 7s
For mossess that no such mode names but a less mathematical name is desired, genchain mode numbering may be used, producing 1st xL ys, 2nd xL ys, and so on.
Sandboxed rewrite: Naming mos intervals and mos degrees
Already deployed on main TAMNAMS page: TAMNAMS#Naming mos intervals
Complements of intervals
The octave complement (or equave complement for mosses that don't have an octave equivalence interval, or simply complement) of a mos interval follows the same logic as the octave complement in regular music theory: in general, for a mos with n pitches, a k-mosstep in its large form has a complement of an (n-k)-mosstep in its small form, and the two intervals are complements of one another. Alternatively, if a specific mos interval is thought of as a quantity of large and small steps, then its complement is the number of steps needed to produce the mos pattern of xL ys itself. Additionally, if a mos interval is also altered by raising it by some number of chromas, its complement will be lowered by the same number of chromas, and vice-versa.
| Interval | Complement | ||
|---|---|---|---|
| Name | Size | Name | Size |
| Perfect 0-mosstep (unison) | 0 | Perfect 7-mosstep (octave) | 3L+4s |
| Major 1-mosstep | L | Minor 6-mosstep | 2L+4s |
| Perfect 2-mosstep | L+s | Diminished 5-mosstep | 2L+3s |
| Major 3-mosstep | 2L+s | Minor 4-mosstep | 1L+3s |
| Major 4-mosstep | 2L+2s | Minor 3-mosstep | 1L+2s |
| Augmented 5-mosstep | 3L+2s | Perfect 2-mosstep | 2s |
| Major 6-mosstep | 3L+3s | Minor 1-mosstep | s |
| Perfect 7-mosstep (octave) | 3L+4s | Perfect 0-mosstep (unison) | 0 |
Sandboxed rewrite: Mos pattern names
Reasoning for names
See: TAMNAMS#Reasoning for the names
The goal of TAMNAMS mos names is to choose memorable but aesthetically neutral names.
Names for small mosses
All names for single-period mosses (mosses of the form xL ys where x and y are coprime) with no more than 5 notes require that some small integer multiple of the period is equal to an octave or a tempered octave, under the reasoning that these mosses are common and broad enough that they may be of interest in non-octave contexts. As such, the names for these mosses are chosen to be extremely general to avoid bias and to avoid being too flavorful, and to allow these names to be reused for such non-octave contexts.
The names of monowood and biwood, for 1L 1s and 2L 2s respectively, requires that an equivalence interval be an octave, whereas the name trivial, also referring to 1L 1s, is equave-agnostic and may be used for non-octave contexts.
Names for multi-period mosses
Multi-period mosses (mosses of the form xL ys where x and y have a greatest common factor of 2 or greater) are given unique names that do not depend on the name of a smaller, octave-specific mos. The inclusion of such mos names was for completeness, which prompted reconsiderations on how these mosses were named. These mosses were formerly named using names that were octave-specific, producing former names such as "antidimanic" and "dipentic".
Names based on a temperament
All names ending in -oid refer to an exotemperament which, when including extreme tunings, covers the entire range of the corresponding octave-period mos, such that many edos with simple step ratios for that mos will correspond to valid tunings, if not by patent val, then with a small number of warts.
Former names like "orwelloid" and "sensoid" were abandoned because the names were too temperament-specific in the sense that even considering extreme tunings didn't cover the whole range of the mos. The remaining temperament-based names have been abstracted or altered heavily, namely "pine", "hyrulic", "jaric", "ekic" and "lemon".
Names for 1L ns mosses
Mosses of the form 1L ns were originally left unnamed as the range for their generator was too broad and such mosses were considered better analyzed as subsets of its (n+1)L 1s mos. An example of this is 1L 6s and 7L 1s, a pair of mosses that are commonly associated with porcupine temperament.
Although the tuning range is very unhelpful for knowing what such mosses will sound like, it is nonetheless useful for describing structure in situations where one does not want to use the mathematical name of 1L ns, especially given that in such situations the tuning will likely be specified somewhere already, hence the inclusion of these mos names.
This inclusion also affected the names of multi-period mosses. Jaric and taric specifically were chosen over bipedal and bimanual because of this, and to a lesser extent, lemon and lime were chosen over antibipentic and bipentic respectively (with their parent mos of 4L 2s named citric for consistency).
The anti- prefix vs the an- prefix for naming 1L ns mosses
The distinction between using the prefixes "anti-" vs "an-" for reversing the number of large vs. small steps is not as trivial as it may sound.
In the case of mosses with six or more notes, as the period is always an octave, there is a very large tuning range for the 1L ns mosses (hence their original omission), but the "anti-" prefix shows that what is significant is that it has the opposite structure to the corresponding nL 1s mos while pointing out the resulting ambiguity of range.
In the case of mosses with five or fewer notes, as the period is not known and therefore could be very small, this is not as much of a concern as fuller specification is likely required anyway, especially in the case of larger periods, so the name should not be tediously long as the name refers to a very simple mos pattern, and for related reasons, the name shouldn't give as much of a sense of one 'orientation' of the structure being more 'primary' than the other, while with mosses with more than five notes, this suggestion of sense is very much intended, because it will almost always make more sense to talk about the (n+1)L 1s child mos of whatever 1L ns mos you want to speak of.
Names for mosses with more than 10 notes
The scope of TAMNAMS name is to give mosses with small note count a notable name. To keep the number of names controlled, only mosses with no more than 10 notes are named. As a result, the names of mosses with 11 and 12 notes were abandoned, notably the names kleistonic, suprasmitonic, m-chromatic, and p-chromatic.
Mosses with more than one name
Some mosses have more than one name, namely tetrawood/diminished (4L 4s), dicoid/zaltertic (7L3s), and superdiatonic/armotonic (7L 2s). Typically, this was due to to an alternate name being suggested to replace an older name, despite the older name being more popular. Either name can be used.
Name-specific reasonings
Superdiatonic and armotonic (7L 2s)
This mos has two names. The name "superdiatonic" has seen some precedent of use on the Xenwiki to refer to the mos 7L 2s despite the use of the name referring specifically to 7L 2s being misattributed to armodue theorists. Superdiatonic is also the first in a series of mos patterns (5+2k)L 2s, of which diatonic (5L 2s, k=0) is the first member. Like 5L 2s, 7L 2s is also a fifth-generated scale and has a structure similar to diatonic in some ways, but is larger. The name "armotonic" is an alternative name for situations where "superdiatonic" is used in a context that does not suggest the mos pattern 7L 2s.
Step ratio spectrum visualization
I wanted to make a table that better visualizes the step ratio ranges as described by TAMNAMS.
Central spectrum
| Central spectrum of step ratios | |||||
|---|---|---|---|---|---|
| Intermediate ranges | Specific step ratios | Notes | |||
| 1:1 (equalized) | Trivial/pathological | ||||
| 1:1 to 1:0 | 1:1 to 2:1 (general soft range) | 1:1 to 3:2 | 1:1 to 4:3 (ultrasoft) | Step ratios especially close to 1:1 may be called pseudoequalized | |
| 4:3 (supersoft) | |||||
| 4:3 to 3:2 (parasoft) | |||||
| 3:2 (soft) | Also called monosoft | ||||
| 3:2 to 2:1 (hyposoft) | 3:2 to 5:3 (quasisoft) | ||||
| 5:3 (semisoft) | |||||
| 5:3 to 2:1 (minisoft) | |||||
| 2:1 (basic) | Also called quintessential | ||||
| 2:1 to 1:0 (general hard range) | 2:1 to 3:1 (hypohard) | 2:1 to 5:2 (minihard) | |||
| 5:2 (semihard) | |||||
| 5:2 to 3:1 (quasihard) | |||||
| 3:1 (hard) | Also called monohard | ||||
| 3:1 to 1:0 | 3:1 to 4:1 (parahard) | ||||
| 4:1 (superhard) | |||||
| 4:1 to 1:0 (ultrahard) | Step ratios especially close to 1:0 may be called pseudocollapsed | ||||
| 1:0 (collapsed) | Trivial/pathological | ||||
Extended spectrum
| Extended spectrum of step ratios | |||||||
|---|---|---|---|---|---|---|---|
| Central ranges | Extended ranges | Specific step ratios | Notes | ||||
| 1:1 (equalized) | Trivial/pathological | ||||||
| 1:1 to 1:0 | 1:1 to 2:1 (general soft range) | 1:1 to 3:2 | 1:1 to 4:3 (ultrasoft) | 1:1 to 6:5 (pseudoequalized) | |||
| 6:5 (semiequalized) | |||||||
| 6:5 to 4:3 (ultrasoft) | |||||||
| 4:3 (supersoft) | Nonextreme range, as detailed by central spectrum | ||||||
| 4:3 to 3:2 (parasoft) | 4:3 to 3:2 (parasoft) | ||||||
| 3:2 (soft) | |||||||
| 3:2 to 2:1 (hyposoft) | 3:2 to 5:3 (quasisoft) | 3:2 to 5:3 (quasisoft) | |||||
| 5:3 (semisoft) | |||||||
| 5:3 to 2:1 (minisoft) | 5:3 to 2:1 (minisoft) | ||||||
| 2:1 (basic) | |||||||
| 2:1 to 1:0 (general hard range) | 2:1 to 3:1 (hypohard) | 2:1 to 5:2 (minihard) | 2:1 to 5:2 (minihard) | ||||
| 5:2 (semihard) | |||||||
| 5:2 to 3:1 (quasihard) | 5:2 to 3:1 (quasihard) | ||||||
| 3:1 (hard) | |||||||
| 3:1 to 1:0 | 3:1 to 4:1 (parahard) | 3:1 to 4:1 (parahard) | |||||
| 4:1 (superhard) | |||||||
| 4:1 to 1:0 (ultrahard) | 4:1 to 10:1 (ultrahard) | 4:1 to 6:1 (hyperhard) | |||||
| 6:1 (extrahard) | |||||||
| 6:1 to 10:1 (clustered) | |||||||
| 10:1 (semicollapsed) | |||||||
| 10:1 to 1:0 (pseudocollapsed) | |||||||
| 1:0 (collapsed) | Trivial/pathological | ||||||
Original table of extended TAMNAMS names (archived)
This is an attempt to describe various mosses that I feel are worth describing, based on experimenting with these scales or for completion. This contains unofficial scale names that try to be as close to existing names as possible and are not meant to be official or standard. The following table shows single-period mosses sorted by generation rather than note count. As of August 2022, much of this section is rendered unnecessary due to TAMNAMS names being reorganized and many scales being renamed, hence this section is kept for archival purposes.
Extended names are denoted with an asterisk. Named 1L ns (monolarge) scales are denoted using italics and are based on its sister scale with the anti- prefix added.
| Mos Family Tree (single-period only), with TAMNAMS Names and extended names | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Progenitor scale | 1st-order child mosses | 2nd-order child mosses | 3rd-order child mosses | 4th-order child mosses | 5th-order child mosses | ||||||
| Steps | Scale name | Steps | Scale name | Steps | Scale name | Steps | Scale name | Steps | Scale name | Steps | Scale name |
| 1L 1s | prototonic*
(currently monowood and trivial) |
1L 2s | antideuteric*
(currently antrial) |
1L 3s | antitetric*
(currently antetric) |
1L 4s | antimanic
(currently pedal) |
1L 5s | antimachinoid*
(currently antimachinoid) |
1L 6s | anti-archeotonic
(currently onyx) |
| 6L 1s | archeotonic | ||||||||||
| 5L 1s | machinoid | 5L 6s | |||||||||
| 6L 5s | |||||||||||
| 4L 1s | manual
(formerly manic) |
4L 5s | gramitonic
(formerly orwelloid) |
4L 9s | |||||||
| 9L 4s | |||||||||||
| 5L 4s | semiquartal | 5L 9s | |||||||||
| 9L 5s | |||||||||||
| 3L 1s | tetric | 3L 4s | mosh | 3L 7s | sephiroid | 3L 10s | |||||
| 10L 3s | |||||||||||
| 7L 3s | dicoid
(formerly dicotonic) |
7L 10s | |||||||||
| 10L 7s | |||||||||||
| 4L 3s | smitonic | 4L 7s | (formerly kleistonic) | 4L 11s | |||||||
| 11L 4s | |||||||||||
| 7L 4s | (formerly suprasmitonic) | 7L 11s | |||||||||
| 11L 7s | |||||||||||
| 2L 1s | deuteric*
(currently trial) |
2L 3s | pentic | 2L 5s | antidiatonic | 2L 7s | balzano
(formerly joanatonic) |
2L 9s | |||
| 9L 2s | |||||||||||
| 7L 2s | superdiatonic | 7L 9s | |||||||||
| 9L 7s | |||||||||||
| 5L 2s | diatonic | 5L 7s | (formerly p-chromatic) | 5L 12s | s-enharmonic* | ||||||
| 12L 5s | p-enharmonic* | ||||||||||
| 7L 5s | (formerly m-chromatic) | 7L 12s | f-enharmonic* | ||||||||
| 12L 7s | m-enharmonic* | ||||||||||
| 3L 2s | antipentic | 3L 5s | checkertonic
(formerly sensoid) |
3L 8s | 3L 11s | ||||||
| 11L 3s | |||||||||||
| 8L 3s | 8L 11s | ||||||||||
| 11L 8s | |||||||||||
| 5L 3s | oneirotonic | 5L 8s | 5L 13s | ||||||||
| 13L 5s | |||||||||||
| 8L 5s | 8L 13s | ||||||||||
| 13L 8 | |||||||||||
Extended mos pattern names (fewer than 5 steps, archived)
As of August 14, 2022, all of these scales have been named. These descriptions are kept for archival purposes.
| Parent scale | 1st-order child scales | 2nd-order child scales | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Steps | Originally proposed name | Current name | Notes | Steps | Originally proposed name | Current name | Notes | Steps | Originally proposed name | Current name | Notes |
| 1L 1s | prototonic, protic, or monowood | monowood and trivial | The progenitor scale of all single-period mosses.
Despite being a monolarge scale, it's also its own sister and is named regardless. The current name "monowood" comes from nL ns scales (such as pentawood for 5L 5s), and is used as a base for such scales. The name trivial comes from the fact that this is a trivial (octave-equivalent) scale, consisting of only its generators. |
1L 2s | antideuterotonic or antideuteric | antrial | One of the child scales of 1L 1s.
Being a monolarge scale, tetric (3L 1s) may be more worth considering as a parent scale. |
1L 3s | antitetric | antetric | Monolarge scale. Similarly to 3L 1s with 1L 2s, 4L 1s may be worth considering as a parent scale. |
| 3L 1s | tetric | tetric | Parent scale to orwelloid (now gramitonic) and semiquartal, the name tetric is assigned similarly to pentic being the parent of diatonic and antidiatonic. | ||||||||
| 2L 1s | deuterotonic or deuteric | trial | One of the child scales of 1L 1s. | 2L 3s | - | pentic | Already established name. | ||||
| 3L 2s | - | antipentic | Already established name. | ||||||||
Proposal: Naming mosses with more than 10 steps (work-in-progress)
This is a system for describing scales beyond the set of named TAMNAMS scales. Both User:Frostburn (User:Frostburn/TAMNAMS Extension) and I have similar systems, with the main difference here being how mosses can be named any number of generations away from a named mos.
To name mosses that have more than 10 notes, rather than giving mosses unique names, names are based on how they're related to another (named) mos.
- A child mos is a chromatic mos. For the child of a named mos, the name is chromatic (mos name), which can be shortened to (mos-prefix)chromatic if the mos has no more than 3 periods. This term collectively refers to 2 possible chromatic mosses, or any one of them.
- A grandchild mos is an enharmonic mos. For the grandchild of a named mos, the name is enharmonic (mos name), which can be shortened to (mos-prefix)enharmonic if the mos has no more than 3 periods. This term collectively refers to 4 possible enharmonic mosses, or any one of them.
- A great-grandchild mos is a subchromatic mos. For the great-grandchild of a named mos, the name is subchromatic (mos name), which can be shortened to (mos-prefix)subchromatic if the mos has no more than 3 periods. This term collectively refers to 8 possible subchromatic mosses, or any one of them. (Tentative name; open to better suggestions.)
A mos that is more than 3 generations away from another mos (eg, a great-great-grandchild mos) or any number of generations from another mos is a mos descendant. For the descendant of a named mos, the name is (mos name) descendant, which can be shortened to (mos-prefix)descendant if the mos has no more than 3 periods. This term collectively refers to any number of descendants of a mos or any single mos descendant regardless of generation, or any one mos descendant. Optionally, the number of generations away from a named parent can be specified, producing the terms nth mos descendant, nth (mos name) descendant, and nth (mos-prefix)descendant, using the algorithm below to find n:
- Let z and w be the number of large and small steps of the parent mos to be found. Assign to z and w the values x and y respectively. Let n = 0, where n is the number of generations away from zL ws.
- Let m1 be equal to max(z, w) and m2 be equal to min(z, w).
- Assign to z the value m2 and w the value m1-m2. Increment n by 1.
- If the sum of z and w is no more than 10, then the parent mos is zL ws and is n generations from the mos descendant xL ys. If not, repeat the process starting at step 2.
As diatonic (5L 2s) doesn't have a prefix, the terms chromatic, enharmonic, and subchromatic by themselves (and with no other context suggesting a non-diatonic mos) refer to 1st (child), 2nd (grandchild), and 3rd (great-grandchild) diatonic descendants. For consistency, mos descendant names apply to mosses whose child mosses exceed 10 notes. Since all mosses ultimately descend from some nL ns mos, every possible descendant up to 5 periods will be related to a named mos.
| 6-note mosses | Chromatic mosses | Enharmonic mosses | |||
|---|---|---|---|---|---|
| Pattern | Name | Patterns | Names | Patterns | Names |
| 1L 5s | antimachinoid | 1L 6s, 6L 1s | n/a | 1A 7B, 6A 7B | n/a |
| 2L 4s | malic | 2L 6s, 6L 2s | n/a | 2A 8B, 6A 8B | n/a |
| 3L 3s | triwood | 3L 6s, 6L 3s | n/a | 3A 9B, 6A 9B | n/a |
| 4L 2s | citric | 4L 6s, 6L 4s | n/a | 4A 10B, 6A 10B | n/a |
| 5L 1s | machinoid | 5L 6s, 6L 5s | mechromatic | 5A 11B, 6A 11B | mechenharmonic |
| 7-note mosses | Chromatic mosses | Enharmonic mosses | |||
| Pattern | Name | Patterns | Names | Patterns | Names |
| 1L 6s | onyx | 1L 7s, 7L 1s | n/a | 1A 8B, 7A 8B | n/a |
| 2L 5s | antidiatonic | 2L 7s, 7L 2s | n/a | 2A 9B, 7A 9B | n/a |
| 3L 4s | mosh | 3L 7s, 7L 3s | n/a | 3A 10B, 7A 10B | n/a |
| 4L 3s | smitonic | 4L 7s, 7L 4s | smichromatic | 4A 11B, 7A 11B | smienharmonic |
| 5L 2s | diatonic | 5L 7s, 7L 5s | chromatic | 5A 12B, 7A 12B | enharmonic |
| 6L 1s | arch(a)eotonic | 6L 7s, 7L 6s | archeoromatic | 6A 13B, 7A 13B | archeoenharmonic |
| 8-note mosses | Chromatic mosses | Enharmonic mosses | |||
| Pattern | Name | Patterns | Names | Patterns | Names |
| 1L 7s | antipine | 1L 8s, 8L 1s | n/a | 1A 9B, 8A 9B | n/a |
| 2L 6s | subaric | 2L 8s, 8L 2s | n/a | 2A 10B, 8A 10B | n/a |
| 3L 5s | checkertonic | 3L 8s, 8L 3s | checkchromatic | 3A 11B, 8A 11B | checkenharmonic |
| 4L 4s | tetrawood; diminished | 4L 8s, 8L 4s | chromatic tetrawood | 4A 12B, 8A 12B | enharmonic tetrawood |
| 5L 3s | oneirotonic | 5L 8s, 8L 5s | oneirochromatic | 5A 13B, 8A 13B | oneiroenharmonic |
| 6L 2s | ekic | 6L 8s, 8L 6s | ekchromatic | 6A 14B, 8A 14B | ekenharmonic |
| 7L 1s | pine | 7L 8s, 8L 7s | pinechromatic | 7A 15B, 8A 15B | pinenharmonic |
| 9-note mosses | Chromatic mosses | Enharmonic mosses | |||
| Pattern | Name | Patterns | Names | Patterns | Names |
| 1L 8s | antisubneutralic | 1L 9s, 9L 1s | n/a | 1A 10B, 9A 10B | n/a |
| 2L 7s | balzano | 2L 9s, 9L 2s | balchromatic | 2A 11B, 9A 11B | balenharmonic |
| 3L 6s | tcherepnin | 3L 9s, 9L 3s | cherchromatic | 3A 12B, 9A 12B | cherenharmonic |
| 4L 5s | gramitonic | 4L 9s, 9L 4s | gramchromatic | 4A 13B, 9A 13B | gramenharmonic |
| 5L 4s | semiquartal | 5L 9s, 9L 5s | chtonchromatic | 5A 14B, 9A 14B | chtonenharmonic |
| 6L 3s | hyrulic | 6L 9s, 9L 6s | hyruchromatic | 6A 15B, 9A 15B | hyrenharmonic |
| 7L 2s | superdiatonic | 7L 9s, 9L 7s | armchromatic | 7A 16B, 9A 16B | armenharmonic |
| 8L 1s | subneutralic | 8L 9s, 9L 8s | bluchromatic | 8A 17B, 9A 17B | bluenharmonic |
| 10-note mosses | Chromatic mosses | Enharmonic mosses | |||
| Pattern | Name | Patterns | Names | Patterns | Names |
| 1L 9s | antisinatonic | 1L 10s, 10L 1s | asinachromatic | 1A 11B, 10A 11B | asinenharmonic |
| 2L 8s | jaric | 2L 10s, 10L 2s | jarachromatic | 2A 12B, 10A 12B | jaraenharmonic |
| 3L 7s | sephiroid | 3L 10s, 10L 3s | sephchromatic | 3A 13B, 10A 13B | sephenharmonic |
| 4L 6s | lime | 4L 10s, 10L 4s | limechromatic | 4A 14B, 10A 14B | limenharmonic |
| 5L 5s | pentawood | 5L 10s, 10L 5s | chromatic pentawood | 5A 15B, 10A 15B | enharmonic pentawood |
| 6L 4s | lemon | 6L 10s, 10L 6s | lemchromatic | 6A 16B, 10A 16B | lemenharmonic |
| 7L 3s | dicoid, zaltertic | 7L 10s, 10L 7s | dicochromatic, zalchromatic | 7A 17B, 10A 17B | dicoenharmonic, zalenharmonic |
| 8L 2s | taric | 8L 10s, 10L 8s | tarachromatic | 8A 18B, 10A 18B | tarenharmonic |
| 9L 1s | sinatonic | 9L 10s, 10L 9s | sinachromatic | 9A 19B, 10A 19B | sinenharmonic |
Names for mos descendants by step ratio
The designations of chromatic, enharmonic, and subchromatic by themselves does not describe a specific mos descendant. To do that, the name of a step ratio range can be prefixed to the terms chromatic, enharmonic, and subchromatic (or (mos-prefix)chromatic, (mos-prefix)enharmonic, and (mos-prefix)subchromatic). Specifying the step ratio is optional, and the names for step ratios can be abbreviated into a one or two-letter prefix. (Frostburn's abbreviations can be used here, too.) These prefixes are used for specific descendants, with the notable exception of soft and hard. For enharmonic mosses, these describe mosses with a step ratio outside the hyposoft and hypohard range. For subchromatic mosses, these describe mosses within the entire soft and hard ranges, producing terminology more specific than just subchromatic but not as specific as the specific step ratio ranges. These prefixes must include a hyphen.
| Parent mos | Chromatic mosses | Enharmonic mosses | Subchromatic mosses | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Steps | L:s range | Steps | Prefix | Abbrev. | L:s range | Steps | Prefix | Abbrev. | L:s range | Steps | Broad prefixes | Specific prefixes | L:s range | ||
| Prefix | Abbrev. | Prefix | Abbrev. | ||||||||||||
| xL ys | 1:1 to 1:0 | (x+y)L xs | soft- | s- | 1:1 to 2:1 | (x+y)L (2x+y)s | soft- | s- | 1:1 to 3:2 | (x+y)L (3x+2y)s | soft- | s- | ultrasoft- | us- | 1:1 to 4:3 |
| (3x+2y)L (x+y)s | parasoft- | ps- | 4:3 to 3:2 | ||||||||||||
| (2x+y)L (x+y)s | hyposoft- | os- | 3:2 to 2:1 | (3x+2y)L (2x+y)s | quasisoft- | qs- | 3:2 to 5:3 | ||||||||
| (2x+y)L (3x+2y)s | minisoft- | ms- | 5:3 to 2:1 | ||||||||||||
| xL (x+y)s | hard- | h- | 2:1 to 1:0 | (2x+y)L xs | hypohard- | oh- | 2:1 to 3:1 | (2x+y)L (3x+y)s | hard- | h- | minihard- | mh- | 2:1 to 5:2 | ||
| (3x+y)L (2x+y)s | quasihard- | qh- | 5:2 to 3:1 | ||||||||||||
| xL (2x+y)s | hard- | h- | 3:1 to 1:0 | (3x+y)L xs | parahard- | ph- | 3:1 to 4:1 | ||||||||
| xL (3x+y)s | ultrahard- | uh- | 4:1 to 1:0 | ||||||||||||
| Balzano (parent) | Chromatic balzano | Enharmonic balzano | Subchromatic balzano | |||||
|---|---|---|---|---|---|---|---|---|
| Steps | Name | Steps | Name | Steps | Name | Steps | Broad name | Specific name |
| 2L 7s | balzano | 9L 2s | s-balchromatic | 9L 11s | s-balenharmonic | 9L 20s | s-balsubchromatic | us-balsubchromatic |
| 20L 9s | ps-balsubchromatic | |||||||
| 11L 9s | os-balenharmonic | 20L 11s | qs-balsubchromatic | |||||
| 11L 20s | ms-balsubchromatic | |||||||
| 2L 9s | h-balchromatic | 11L 2s | oh-balenharmonic | 11L 13s | h-balsubchromatic | mh-balsubchromatic | ||
| 13L 11s | qh-balsubchromatic | |||||||
| 2L 11s | h-balenharmonic | 13L 2s | ph-balsubchromatic | |||||
| 2L 13s | uh-balsubchromatic | |||||||
Names for mos descendants with more than 5 periods
To name mos descendants with more than 5 periods, the names for wood mosses are extended to hexawood, heptawood (or septawood), octawood, nonawood (or enneawood), and decawood. Beyond that, the naming scheme becomes 11-wood, 12-wood, and so on, and mosses are referred to chromatic (number)-wood, enharmonic (number)-wood, and subchromatic (number)-wood. The term (number)-wood descendants is also used, and to refer to nth (number)-wood descendants, the algorithm is used below to find the number of generations:
- Let z and w be the number of large and small steps of the parent mos to be found. Assign to z and w the values x and y respectively. Let n = 0, where n is the number of generations away from zL ws.
- Let m1 be equal to max(z, w) and m2 be equal to min(z, w).
- Assign to z the value m2 and w the value m1-m2. Increment n by 1.
- If both z and w are equal to 1, then the parent mos is nL ns and is n generations from the mos descendant xL ys. If not, repeat the process starting at step 2.
| Mos | Name | Prefix | Abbrev. |
|---|---|---|---|
| 6L 6s | hexawood | hexwud- | hw |
| 7L 7s | septawood or heptawood | sepwud- or hepwud- | sw or hw |
| 8L 8s | octawood | octwud- | ow |
| 9L 9s | nonawood or enneawood | nonawud- or ennwud- | nw or enw |
| 10L 10s | decawood | dekwud- | dkw |
Other names (in-progress)
- n-monolarge or monolarge - Refers to any mos that is of the form 1L ns. These mosses form an infinite mos family that is itself a singular line. This family includes 1L 1s, 1L 2s, 1L 3s, and so on.
- n-polylarge or polylarge - Refers to any mos of the form xL (nx+y)s that is along the pseudocollapsed range of step ratios for a mos xL ys. These mosses form an infinite linear family, similar to monolarge mosses. One example of this is 2L 1s, 2L 3s, 2L 5s, 2L 7s, 2L 9s, and so on.
Reasoning for names
The names for chromatic scales are based on former names for the child mosses of diatonic (5L 2s) - p-chromatic for 5L 7s and m-chromatic for 7L 5s - and was generalized to chromatic mos. The term enharmonic is already in use to describe the grandchild mosses of diatonic, and so was generalized to enharmonic mos. The term subchromatic is a term coined by Mike Battaglia to describe a scale that is more chromatic than either chromatic or enharmonic, and is generalized to subchromatic mos.
The format of adding a mos's prefix to the terms descendant, chromatic, enharmonic, and subchromatic is best applied to mosses that have no more than three periods. With mosses that descend directly from nL ns mosses especially (4L 4s and above), this is to keep names from being too cumbersome (eg, chromatic (number)-wood instead of (number)-woodchromatic).
Various people have suggested the use of p- and m- as prefixes to refer to specific chromatic mosses, as well as the use of f- and s- for enharmonic mosses. Generalizing the pattern to 3rd mos descendants reveals an issue where the letters started to diverge from one another, notably where m- is no longer next to p- and f- and s- are no longer along the extremes. Rather than to use these letters and to maintain temperament agnosticism, prefixes based on step ratios are used instead.
| Diatonic scale | Chromatic mosses | Enharmonic mosses | Subchromatic mosses | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Steps | Notable temperament | Prefix | Steps | Notable temperament | Prefix | Steps | Notable temperament | Prefix | |
| 5L 2s | 7L 5s | meantone | m- | 7L 12s | flattone | f- | 7L 19s | tridecimal | t- |
| 19L 7s | flattone | f- | |||||||
| 12L 7s | meantone | m- | 19L 12s | meanpop | m- | ||||
| 12L 19s | huygens | h- | |||||||
| 5L 7s | pythagorean | p- | 12L 5s | pythagorean | p- | 12L 17s | pythagorean | p- | |
| 17L 12s | gentle | g- | |||||||
| 5L 12s | superpyth | s- | 17L 5s | superpyth | s- | ||||
| 5L 17s | ultrapyth | u- | |||||||
The temperament-based prefixes may be used specifically for diatonic descendants as alternatives to the prefixes based on step ratios, effectively bringing back the names of p-chromatic and m-chromatic.
Suggested changes for mos pattern names (work-in-progress)
This section describes changes to existing TAMNAMS names that I would make. Reasons:
- Some names are still based on a temperament (mainly the -oid names), so those are either replaced with a new name or at least altered so the references are more indirect.
- There were Discord users with whom I shared a similar sentiment regarding the names of certain scales, mainly the mosses with the anti- prefix and the scales antidiatonic and superdiatonic.
- Some names are too long (in my opinion).
The choice of names are not perfect and some may have issues. Some name suggestions went through different versions. This section is meant to start a discussion on alternate names should a need come up for it.
| Changes to names to reduce or remove references to temperaments | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Mos | Current name | Suggested name(s) | Old suggestions | Reasoning | Possible issues | ||||
| Name | Prefix | Abbrev. | Name | Prefix | Abbrev. | ||||
| 5L 1s | machinoid | mech- | mech | mechatonic | unchagned | unchagned | A more indirect reference to machine temperament. | Still references machine temperament. May also reference mechanism temperament. May be too minor of a modification. | |
| 3L 7s | sephiroid | seph- | seph | sephirotonic or sephiratonic | unchagned | unchagned | septonic | Rather than alluding to sephiroth temperament, the name should allude to Peter Kosmorsky's Tractatum de Modi Sephiratorum (A Treatise on the Modes of the Sephirates), whose name ultimately comes from the sefirot. The document describes several edos that are said to contain the "modi sephiratorum" (sephirate modes). Therefore, instead of the name "sephiroid", suggesting that the mos pattern resembles the modi sephiratorum, the mos pattern is the modi sephiratorum, hence the mosname "sephirotonic". | May still reference sephiroth temperament. For a more indirect reference, an alternate transliteration of סְפִירוֹת (sefirot) may be used instead.
New name is longer than the old name. |
| 7L 3s | dicoid and zaltertic | dico- and zal- | dico and zal | zaltertic | zal- | zal | As of writing, there are two names. I would favor zaltertic over dicoid in that it removes a name that suggests a temperament. | Central zalzalian thirds (another name for neutral thirds) are not the scale's bright generator, but are produced by the scale. | |
| Changes to names that bear the anti- prefix | |||||||||
| Mos | Current name | Suggested name(s) | Old suggestions | Reasoning | Possible issues | ||||
| Name | Prefix | Abbrev. | Name | Prefix | Abbrev. | ||||
| 1L 5s | antimachinoid | amech- | amech | selenite | sel- | sel | selenic | Shorter name. An indirect reference to luna temperament; "selene" is Greek for "moon". The name "selenite" follows the same pattern of 1L 6s being named after a type of gemstone. | Pun. |
| 1L 7s | antipine | apine- | apine | spinel | spin- | spin | alpine, stelanic | Shorter names. These names follow in the same spirit as "onyx" for 1L 6s in the following ways:
|
Pun. The names suggested don't typically rhyme with the words they're trying to rhyme with or reference, ruining the joke. |
| 1L 8s | antisubneutralic | ablu- | ablu | agate | aga- or agat- | aga | mineric | ||
| 1L 9s | antisinatonic | asina- | asi | olivine | oliv- | oliv | parivalic, alentic | ||
| Changes to names that bear other prefixes | |||||||||
| Mos | Current name | Suggested name(s) | Old suggestions | Reasoning | Possible issues | ||||
| Name | Prefix | Abbrev. | Name | Prefix | Abbrev. | ||||
| 2L 5s | antidiatonic | pel- | pel | pelotonic or peltonic | unchagned | unchagned | pelic | From "pelog" and "armodue". The proposed names are to make both scales more distinct from diatonic. These names must be changed together if possible. The term "superdiatonic" was misattributed to armodue theorists (the term cannot be found anywhere on the armodue website) and may have meant something other than 7L 2s. (Clarification needed.) | The connection to diatonic may be beneficial to some musicians. Additionally, the mode names commonly used for both mosses are those from diatonic (lydian, ionian, etc) with the anti- and super- prefixes added. Despite misattribution, the name "superdiatonic" commonly refers to 7L 2s. A possible compromise is to use both names (some mosses already have more than one name).
New names reference pelog tuning and armodue theory. Hairtonic ("pelo" is Spanish for "hair"). |
| 7L 2s | superdiatonic | arm- | arm | armotonic | unchagned | unchagned | armic | ||
| 8L 1s | subneutralic | blu- | blu | azurtonic | azu- or unchanged | azu or unchanged | azuric | An indirect reference to bleu temperament; azure is a specific shade of blue. Simplified name. Also, the sub- prefix may falsely suggest another scale called "(prefix)neutralic", similar to how subaric (2L 6s) is the parent to both jaric (2L 8s) and taric (8L 2s). | New name is referencing a temperament, albeit indirectly. The sub- prefix reasoning may be a stretch, since subaric, jaric, and taric are the only mosses related this way. |
| 2L 6s | subaric | subar- | subar | baric | bara- | bar | Rhymes perfectly with jaric and taric. May also mean "basic -aric", as this mos with a basic step ratio (L:s=2:1) cannot produce jaric or taric, or rather, produces both but equalized. | Too minor of a modification. The use of "bar" as an abbreviation may be problematic ("bar" may also mean "measure" in sheet music). | |
Aesthetic rules
These are the rules that attempt to justify the logic behind much of the name suggestions. There are, of course, exceptions to these rules, as some names are arguably too memorable to change.
- Names for single-period mosses with 5 or fewer notes are the most general names in the sense that they're not limited to an octave period and end with -ic or -al. These should be the only mosses that contain the anti- prefix, shortened to an-. (Exception: monowood is octave-specific and does not end with -ic or -al.)
- An extreme alternative to rule 1 is to say that all mosses named under rule 1 should end with -al, but this requires renaming more mosses (antetral, tetral, pental, anpental) for arguably little gain.
- Names for single-period mosses not of the form 1L ns end with -tonic, suggesting that these are octave-specific and reference a specific interval, a notable pre-TAMNAMS or other temperament-agnostic name, or indirectly reference a temperament if all other options are exhausted. (Exceptions: mosh, semiquartal, zaltertic, balzano, and pine don't end with -tonic.)
- Names for mosses of the form 1L ns with 6 or more notes are named after gemstones and minerals, following the spirit of 1L 6s being named onyx. These are named differently than those named using the previous rule as these mosses have too broad a tuning range to even suggest a single temperament.
- Names for multi-period mosses end with -ic and always refer to an octave-equivalent scale. (Execptions: lemon, lime, tcherepnin, and all the -wood scales don't end with -ic.)
- With the exception of mosses named under rule 1, no mosses should be named in a way that they contain additional prefixes such as anti-, sub-, or super-. (Exception: semiquartal bears the semi- prefix, but its mosprefix is chton-).
Other name changes:
- Antipentic -> anpentic; follows names of other small mosses where an- is used as a shortened form of anti-.
| Single-period mosses | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Mos | Name | Mos | Name | Mos | Name | Mos | Name | Mos | Name | Mos | Name | Mos | Name | Mos | Name | Mos | Name |
| 1L 1s | trivial
monowood |
1L 2s | antrial | 1L 3s | antetric | 1L 4s | pedal | 1L 5s | selenite | 1L 6s | onyx | 1L 7s | spinel | 1L 8s | agate | 1L 9s | olivine |
| 9L 1s | sinatonic | ||||||||||||||||
| 8L 1s | azurtonic | ||||||||||||||||
| 7L 1s | pine | ||||||||||||||||
| 6L 1s | arch(a)eotonic | ||||||||||||||||
| 5L 1s | mechatonic | ||||||||||||||||
| 4L 1s | manual | 5L 4s | semiquartal | ||||||||||||||
| 4L 5s | gramitonic | ||||||||||||||||
| 3L 1s | tetric | 4L 3s | smitonic | ||||||||||||||
| 3L 4s | mosh | 7L 3s | zaltertic | ||||||||||||||
| 3L 7s | sephiratonic | ||||||||||||||||
| 2L 1s | trial | 3L 2s | anpentic | 3L 5s | checkertonic | ||||||||||||
| 5L 3s | oneirotonic | ||||||||||||||||
| 2L 3s | pentic | 5L 2s | diatonic | ||||||||||||||
| 2L 5s | pelotonic | 7L 2s | armotonic | ||||||||||||||
| 2L 7s | balzano | ||||||||||||||||
| 2-period mosses | |||||||||||||||||
| Mos | Name | Mos | Name | Mos | Name | Mos | Name | ||||||||||
| 2L 2s | biwood | 2L 4s | malic | 2L 6s | baric | 2L 8s | jaric | ||||||||||
| 8L 2s | taric | ||||||||||||||||
| 6L 2s | ekic | ||||||||||||||||
| 4L 2s | citric | 6L 4s | lemon | ||||||||||||||
| 4L 6s | lime | ||||||||||||||||
| 3-period mosses | |||||||||||||||||
| Mos | Name | Mos | Name | ||||||||||||||
| 3L 3s | triwood | 3L 6s | tcherepnin | ||||||||||||||
| 6L 3s | hyrulic | ||||||||||||||||
| 4-period mosses | |||||||||||||||||
| Mos | Name | ||||||||||||||||
| 4L 4s | tetrawood | ||||||||||||||||
| 5-period mosses | |||||||||||||||||
| Mos | Name | ||||||||||||||||
| 5L 5s | pentawood | ||||||||||||||||